Abstract

Significant progress has been achieved in recent years with the development of high-dimensional permutationally invariant analytic Born-Oppenheimer potential-energysurfaces, making use of polynomial invariant theory. In this work, we have developed a generalization of this approach which is suitable for the construction of multi-sheeted multi-dimensional potential-energysurfaces exhibiting seams of conical intersections. The method avoids the nonlinear optimization problem which is encountered in the construction of multi-sheeted diabatic potential-energysurfaces from ab initio electronic-structure data. The key of the method is the expansion of the coefficients of the characteristic polynomial in polynomials which are invariant with respect to the point group of the molecule or the permutation group of like atoms. The multi-sheeted adiabatic potential-energysurface is obtained from the Frobenius companion matrix which contains the fitted coefficients. A three-sheeted nine-dimensional adiabatic potential-energysurface of the 2T2 electronic ground state of the methane cation has been constructed as an example of the application of this method.

Received 19 March 2013Accepted 20 May 2013Published online 10 June 2013

Acknowledgments:

This work was supported by a research grant of the Deutsche Forschungsgemeinschaft for D.O. Computing resources provided by the Leibniz Rechenzentrum of the Bavarian Academy of Sciences are gratefully acknowledged.

Article outline:I. INTRODUCTIONII. DESCRIPTION OF THE METHODIII. APPLICATION: THE PE SURFACE OF THE 2T2 ELECTRONIC GROUND STATE OF A. Calculation of the ab initio data setB. Fitting procedureIV. SUMMARY AND CONCLUSIONS